A passive filter uses a resistor with a reactive component — a capacitor or inductor — to pass some frequencies and block others. The dividing line is the cutoff (corner) frequency, where the output has dropped to −3 dB (70.7% of the input voltage). For first-order RC and RL filters this frequency depends only on the resistor and the reactive part; an RLC filter adds resonance, with a centre frequency, a quality factor and a defined bandwidth.
Reviewed: June 19, 2026 · Author: Naveen P N, Founder — AI Calculator · Verified against: Wikipedia: Low-pass filter and standard circuit texts.
The filter formulas
Whether an RC stage is low-pass or high-pass depends only on where you take the output, not on the cutoff formula: across the capacitor gives low-pass, across the resistor gives high-pass. For an RL filter the roles swap. The time constant τ = RC (or L/R) and the cutoff are linked by fc = 1/(2πτ).
Worked example — an audio anti-alias filter
Scenario: A low-pass RC filter to roll off above 16 kHz before an ADC, using a 1 kΩ resistor.
With a standard 10 nF capacitor the actual cutoff is fc = 1/(2π × 1000 × 1e−8) = 15.9 kHz — close enough. For a sharper roll-off than 20 dB/decade, cascade stages or use an active filter. For the resonant (RLC) version, see the resonant frequency calculator.
Frequently Asked Questions
fc = 1 / (2π × R × C). R = 1 kΩ, C = 100 nF gives ≈1592 Hz. The same formula gives the corner of both low-pass and high-pass RC filters.
fc = R / (2π × L). R = 100 Ω, L = 10 mH gives ≈1592 Hz. A larger inductor lowers the cutoff.
It is the −3 dB (half-power, 0.707 voltage) point. A low-pass passes below it; a first-order filter rolls off at 20 dB/decade above it. A high-pass does the opposite.
f0 = 1 / (2π√(L×C)) — the same as resonance. Selectivity Q = (1/R)√(L/C) (series), bandwidth = f0 ÷ Q.
Low-pass passes frequencies below cutoff; high-pass passes those above. For RC, output across the capacitor = low-pass, across the resistor = high-pass; the cutoff formula is identical.